Well, let's say you are referring to a Colt Model 1873 Single Action Army.
The patent dates should read:
PAT. SEPT. 19, 1871
JULY 2, 72, JAN 19, 75
The Rampant Colt enclosed by a full circle is correct. As a side note, I am happy to see the full circle is still present. Leaves me to believe the gun hasn't been pricked with.
Your serial number indicates manufacture in early 1897, which makes your gun officially an Antique. The serial number should appear in the two places you've mentioned, and on the bottom of the butt. The grip panels may have the last few digits scratched into them as well. The cylinder should NOT be numbered in this year range.
Standard barrel lengths were 4 3/4", 5 1/2" and 7 1/2". Many other lengths were available on order, and bring extra value if substantiated.
We'll assume standard SAA configuation, not Bisley.
Although your gun was slightly before Colt approved the model for use with smokeless powder, you should have the lateral base pin latch associated with smokeless frames. The 'black powder' frame was phased out in 1892.
I could go on and on, but let's cut to the chase. Assuming you have an honest, un-fiddled with Colt SAA in .45 Colt, made in 1897, with no special features, in about 10% original finish....at least $1500. If any rare features or verifiable special order features, double it - plus.
The autonomic nervous system provides for involuntary muscle function - the work of breathing, digestion, and so forth. On some folks, that's a pure waste of ingenuity.